A090783 a(n) can be expressed as the difference of the squares of consecutive primes in just three distinct ways.

1848, 6888, 14280, 16008, 19152, 36120, 112728, 116832, 129480, 139080, 176520, 190632, 190968, 199752, 216840, 236208, 252120, 274848, 303960, 314160, 340368, 363720, 435792, 458280, 503160, 513240, 686160, 688680, 698880, 712680, 721560

Offset: 1

Author

Ray G. Opao, Feb 08 2004

Keywords

• nonn

Examples

			1848 = 463^2 - 461^2 = 233^2 - 229^2 = 157^2 - 151^2.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 3091 terms from Robert Israel)

Crossrefs

Cf. A078667, A090784, A090785, A091878.

Programs

Maple

N:= 10^6: # to get all terms <= N
V:= Vector(N/4):
p:= 3:
while p < N/2 do
  q:= p;
  p:= nextprime(p);
  r:= (p^2-q^2)/4;
  if r <= N/4 then
    V[r]:= V[r]+1
  fi
od:
map(`*`,select(t -> V[t]=3, [$1..N/4]),4); # Robert Israel, Aug 13 2018

PARI

is(n) = my(i=0, v=[]); forprime(p=5, n, v=[precprime(p-1), p]; if(v[2]^2-v[1]^2==n, i++)); i==3 \\ Felix Fröhlich, Aug 13 2018

Extensions

More terms from Ray Chandler, Feb 11 2004